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vfiekz [6]
3 years ago
12

What is the mean of the values in the dot plot? Enter your answer in the box.

Mathematics
2 answers:
Hitman42 [59]3 years ago
7 0

Answer:

19.5

Step-by-step explanation:

16,17,17,17,17,19,19,19,19,21,22,22,23,25

16+17+17+17+17+19+19+19+19+21+22+22+23+25=273

273 divided by 14 = 19.5

kherson [118]3 years ago
3 0

Answer:

19.5

Step-by-step explanation:

To find mean, you have to add all of the numbers in the data set together. After that, take the number of numbers in the data set, and divide that by the all of the numbers added up.

So for this situation, it's on a graph, so you have to make a note of the dots on the points. The data set should look like this:

16, 17, 17, 17, 17, 19, 19, 19, 19, 21, 22, 22, 23, 25 .

When added together, the total is 273.

From there, divide 248 by the 14 numbers in the data set, and you'll get 19.5, which is the mean.

brainliest is always epic if you want ;)

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A+b=180<br> A=-2x+115<br> B=-6x+169<br> What is the value of B?
natulia [17]
The answer is:  " 91 " .   
___________________________________________________
                    →    " B = 91 " .
__________________________________________________ 

Explanation:
__________________________________________________
Given:  
__________________________________________________
    "  A +  B = 180 " ;

  "A =  -2x + 115 " ;   ↔  A =  115 − 2x ;  

  "B = - 6x + 169 " ;  ↔  B = 169 − 6x ;  
_____________________________________________________
METHOD 1)
_____________________________________________________
Solve for "x" ; and then plug the solved value for "x" into the expression given for "B" ; to  solve for "B"
_____________________________________________________

(115 − 2x) + (169 − 6x) = 

  115 − 2x + 169 − 6x = ?

→ Combine the "like terms" ;  as follows:

      + 115 + 169 = + 284 ; 

 − 2x − 6x = − 8x ; 
_________________________________________________________
And rewrite as:

 " − 8x + 284 " ; 
_________________________________________________________
   →  " - 8x + 284 = 180 " ; 

Subtract:  "284" from each side of the equation:

  →  "  - 8x + 284 − 284 = 180 − 284 " ; 

to get:

 →  " -8x = -104 ; 

Divide EACH SIDE of the equation by "-8 " ; 
    to isolate "x" on one side of the equation; & to solve for "x" ; 

→ -8x / -8 = -104/-8 ; 

→  x = 13
__________________________________________________________
Now, to find the value of "B" :
__________________________________________________________
  "B = - 6x + 169 " ;  ↔  B = 169 − 6x ;  

↔  B = 169 − 6x ;  

         = 169 − 6(13) ;   ===========> Plug in our "solved value, "13",  for "x" ;

         = 169 − (78) ; 

         = 91 ;

   B   = " 91 " .
__________________________________________________
The answer is:  " 91 " . 
____________________________________________________
     →     " B = 91 " . 
____________________________________________________
Now;  let us check our answer:
____________________________________________________
               →   A + B = 180 ;  
____________________________________________________
Plug in our "solved answer" ; which is "91", for "B" ;  as follows:
________________________________________________________

→  A + 91 = ? 180? ;  

↔  A = ? 180 − 91 ? ; 

→  A = ?  -89 ?  Yes!
________________________________________________________
→  " A =  -2x + 115 " ;   ↔  A =  115 − 2x ;  

Plug in our solved value for "x"; which is: "13" ; 

" A = 115 − 2x " ; 

→  A = ? 115 − 2(13) ? ;

→  A = ? 115 − (26) ? ; 

→  A = ? 29 ? Yes!
_________________________________________________ 
METHOD 2)
_________________________________________________
Given:  
__________________________________________________
    "  A +  B = 180 " ;

  "A =  -2x + 115 " ;   ↔  A =  115 − 2x ;  

  "B = - 6x + 169 " ;  ↔  B = 169 − 6x ; 

→  Solve for the value of "B" :
_______________________________________________________
 A + B = 180 ;  

→ B = 180 − A ; 

→ B = 180 − (115 − 2x) ; 

→ B = 180 − 1(115 − 2x) ;  ==========> {Note the "implied value of "1" } ; 
__________________________________________________________
Note the "distributive property" of multiplication:__________________________________________________  a(b + c)  = ab +  ac ;  <u><em>AND</em></u>:
  a(b − c)  = ab − ac .________________________________________________________
Let us examine the following part of the problem:
________________________________________________________
              →      " − 1(115 − 2x)  " ; 
________________________________________________________

→  "  − 1(115 − 2x) " = (-1 * 115) − (-1 * 2x) ;

                                =  -115 − (-2x) ;
                         
                                =  -115  +  2x ;        
________________________________________________________
So we can bring down the:  " {"B = 180 " ...}"  portion ; 

→and rewrite:
_____________________________________________________

→  B = 180 − 115 + 2x ; 

→  B = 65 + 2x ; 
_____________________________________________________
Now;  given:   "B = - 6x + 169 " ;  ↔  B = 169 − 6x ; 

→ " B =  169 − 6x  =  65 + 2x " ; 
______________________________________________________
→  " 169 − 6x  =  65 + 2x "

Subtract "65" from each side of the equation;  & Subtract "2x" from each side of the equation:

→  169 − 6x − 65 − 2x  =  65 + 2x − 65 − 2x ; 

to get:

→   " - 8x + 104 = 0 " ;
 
Subtract "104" from each side of the equation:

→   " - 8x + 104 − 104 = 0 − 104 " ;

to get: 

→   " - 8x = - 104 ;

Divide each side of the equation by "-8" ; 
   to isolate "x" on one side of the equation; & to solve for "x" ; 

→  -8x / -8  = -104 / -8 ; 

to get:

→  x =  13 ; 
______________________________________________________

Now, let us solve for:  " B " ;  → {for which this very question/problem asks!} ; 

→  B = 65 + 2x ;  

Plug in our solved value, " 13 ",  for "x" ; 

→ B = 65 + 2(13) ; 

        = 65 + (26) ;  

→ B =  " 91 " .
_______________________________________________________
Also, check our answer:
_______________________________________________________
Given:  "B = - 6x + 169 " ;   ↔  B = 169 − 6x = 91 ; 

When "x  = 13 " ; does: " B = 91 " ? 

→ Plug in our "solved value" of " 13 " for "x" ;

      → to see if:  "B = 91" ; (when "x = 13") ;

→  B = 169 − 6x ; 

         = 169 − 6(13) ; 

         = 169 − (78)______________________________________________________
→ B = " 91 " . 
______________________________________________________
6 0
3 years ago
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